Spectroscopic study of laser-induced plasma in aqueous media

Laser-induced plasma on the surface of ionic solutions of Ca⁺⁺ is studied spectroscopically. The dependence with time and space of the electronic density and temperature is carried out. The temporal and spatial evolution of line intensity 3934 Å are measured, and its behaviour is simulated by a simple theoretical approach based on electron ion recombination processes.     

Electrochemical Characterization of Nickel Electrodes in Phosphate and Carbonate Electrolytes in View of Assessing a Medical Diagnostic Device for the Detection of Early Diabetes

In view of optimizing a multi‐electrode device using proprietary technology for noninvasive assessment of eccrine sweat gland activity and thus the early detection of diabetes, we thoroughly explored the electrochemical behavior of a nickel electrode in a three‐electrode set up combining a nickel counter electrode and a nickel pseudo‐reference electrode in synthetic buffered phosphate and carbonate solutions in presence of chloride, lactate and urea that mimic the composition of physiological sweat. This approach provides insight into the origin of the onset of responses measured upon the application of low voltage potential with variable amplitudes to Ni electrodes on the skin. For low voltage amplitude of ca. ΔE=0.6 V, the electrochemical reactions measured at the electrodes are those related to the oxidation of Ni leading to the formation of a passive layer, as well as the reduction of this passive layer. For voltage amplitude higher than 1 V, or current densities higher than 1 mA/cm², the breakdown of the passive layer becomes the main electrochemical anodic reaction, while its reduction and the electrolytic solution govern the cathode reactions. This brings explanation of the nonlinear current‐voltage features measured during the clinic tests. Finally, the obtained results make possible the definition of the experimental electrochemical conditions where the Ni electrodes can be renewed.     

Weighted Hardy inequality with higher dimensional singularity on the boundary

Let \(\Omega \) be a smooth bounded domain in \(\mathbb R ^N\) with \(N\ge 3\) and let \(\Sigma _k\) be a closed smooth submanifold of \(\partial \Omega \) of dimension \(1\le k\le N-2\) . In this paper we study the weighted Hardy inequality with weight function singular on \(\Sigma _k\) . In particular we provide necessary and sufficient conditions for existence of minimizers.     

A generalization of a theorem by Bigard–Keimel and Conrad–Diem

Let G be an archimedean ℓ-group and \mathfrakP(G){\mathfrak{P}(G)} denote the set of all polar preserving bounded group endomorphisms of G. Bigard and Keimel in [Bull. Soc. Math. France 97 (1969), 381–398] and, independently, Conrad and Diem in [Illinois J. Math. 15 (1971), 222–240] proved that \mathfrakP(G){\mathfrak{P}(G)} is an archimedean ℓ-group with respect to the pointwise addition and ordering. This classical result is extended in this paper to certain sets of disjointness preserving bounded homomorphisms on archimedean ℓ-groups.     

Maximal ideals of disjointness preserving operators

Let L and M be vector lattices with M Dedekind complete, and let Lr(L,M) be the vector lattice of all regular operators from L into M. We introduce the notion of maximal order ideals of disjointness preserving operators in Lr(L,M) (briefly, maximal δ-ideals of Lr(L,M)) as a generalization of the classical concept of orthomorphisms and we investigate some aspects of this ‘new’ structure. In this regard, various standard facts on orthomorphisms are extended to maximal δ-ideals. For instance, surprisingly enough, we prove that any maximal δ-ideal of Lr(L,M) is a vector lattice copy of M, when L, in addition, has an order unit. Moreover, we pay a special attention to maximal δ-ideals on continuous function spaces. As an application, we furnish a characterization of lattice bimorphisms on such spaces in terms of weigthed composition operators.     

Inversion formulas for q-Riemann-Liouville and q-Weyl transforms

We study fractional transforms associated with q-Bessel operator which is useful to inverse q-Riemann-Liouville and q-Weyl transforms.